A signature on a painting is important for several reasons. It shows that you are taking ownership or copyright of the artwork, of course, but adding your name to a painting is like adding a stamp to it that reads "finished." It's a sign that you're satisfied with the composition, and you no longer consider it a work in progress.
Why Sign a Painting
While it's not a legal requirement, if you don't add your name to a painting, it will be difficult for a viewer to identify you as the artist. You may argue that you have a very familiar style that people will recognize, but unless you are already famous, you may not get the credit you deserve.
If a piece of art is hanging in a gallery, it'll have a label with your name on it, but if it's in someone's home, the owner may forget you are the artist. Or those who purchased it might know, but their heirs might not, especially if it's not identified in their will.
The most important thing is that people must be able to read your signature. An illegible signature isn't a sign that you're incredibly creative, and it doesn't add a level of intrigue to the painting. You're the artist, so let it be known. That said, try to avoid making it look like you're using a stamp—ideally, it will not detract from the painting.
You don't have to sign your full name on the front of the painting, and you can opt to put your initials instead. If you take this approach, it's helpful to put your full name on the back of the painting. The same applies if you use a symbol or an artist's monograph—people need to have some way of knowing who the marks represent.
Adding a Date
In most cases, adding the date you finished a painting is helpful, though it needn't be next to your signature on the front. When you first start as an artist, you'll probably be able to remember what year you painted a particular piece. But after you've been painting for several years, you may be less confident as to when you created the work.
Serious collectors and galleries like to be able to see how a painter's work developed over the years, so it's advisable to get into the habit now of dating your work. You can opt to write the date on the back of your canvas or frame. Some artists choose to put only the year on the front and the month and year you completed it on the back.
Putting a date on a painting does not limit your potential to sell it. Art isn't like food—it has no sell-by date. If buyers wanted only the newest and latest works, then there wouldn't be an auction market for older paintings.
Where you sign your painting is up to you, though traditionally, a signature is put toward one of the bottom corners. Be consistent about where you put your name so that when people next encounter a painting they think is by you, they will know exactly where to check.
Signing Tools and Mediums
Often artists choose to apply the same medium used in the artwork to create their signatures, whether it's pastel, watercolor, acrylic, etc. You can sign the work before you clean your brushes and palette for the last time so you've got a suitable color on hand that will blend in with the work. A thin rigger brush is a good size and shape for signatures.
Having your signature "match" the painting, rather than having it look like a later addition, also makes it less likely that someone will question the authenticity of the work at a future date. Avoid adding your signature on top of a layer of varnish, as it can stand out and look like you forgot to sign it in time.
Maiden Name vs. Married Name
It's a matter of individual preference if you choose to use your maiden name or married name to sign your painting. If you're already known professionally by a maiden name, it would be easier to keep it, because changing your name will require you to remarket yourself. Or if both partners are artists, then sometimes people prefer to have different names to avoid comparison.
If you feel strongly about using your married name, switching is possible; it will just require more effort. In some cases, your new name may be catchier or easier to remember, so the work to rebrand yourself may be worth it in the long run.
When you create a limited edition print, it's helpful to indicate how many prints were made and the number of that particular print. For example, you would include 3/25 (the third print of a total of 25) along with your signature. Some buyers will be attracted to the idea that there are only a few replicas, potentially making the work more valuable in the future.